lastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the
top. Ignoring the thickness of the plastic sheet, determine:
The area of the sheet required for making the box.
The cost of sheet for it, if a sheet measuring 1m² costs * 20.
Answers
Answer:
Length of plastic box (l) = 1.5 m
Width of plastic box (b) = 1.25 m
Depth of plastic box (h) = 0.65 m
(i) The area of sheet required to make the box is equal to the surface area of the box excluding the top.
Surface area of the box = Lateral surface area + Area of the base
= 2(l+b)×h + (l×b)
= 2[(1.5 + 1.25)×0.65] + (1.5 × 1.25) m²
= (3.575 + 1.875) m²
= 5.45 m²
The sheet required required to make the box is 5.45 m²
(ii) Cost of 1 m² of sheet = Rs 20
∴ Cost of 5.45 m² of sheet = Rs (20 × 5.45) = Rs 109
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Question :-
A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1m2 costs ₹20.
Answer :-
(i) Here, length (l) = 1.5 m, bread th(b) = 1 .25 m
and height (h) = 65 cm = 65/100 m = 0.65 m
∵ It is open from the top.
∴ Its surface area
= [Lateral surface area] + [Base area]
= [2(1 + b)h] + [lb]
= [2(1.50 + 1.25)0.65] m2 + [1.50 x 1.25] m2
= [2 x 2.75 x 0.65] m2 + [1.875] m2
= 3.575 m2+ 1.875 m2 = 5.45 m2
∴ Area of the sheet required for making the box = 5.45 m2
(ii) Cost of 1 m2 sheet = Rs. 20
Cost of 5.45 m2 sheet = Rs. (20 x 5.45)
= Rs. 109
Hence, cost of the required sheet = Rs. 109
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